Abstraction Refinement-Based Verification of Timed Automata

Tamás Tóth, István Majzik
2021 Zenodo  
Formal methods are mathematical techniques that enable the rigorous specification and verification of hardware and software systems, typically in design time. Formal verification techniques are formal methods for reasoning about the correctness of systems with respect to a formal specification or property. Model checking is an automatic formal verification technique that is based on exhaustive traversal of the design model's state space. Its main advantage to more conventional verification
more » ... ds (e.g. testing) is that it is not only able to detect faults in faulty systems, but can also show that a correct system is fault-free. However, a major difficulty in the successful application of model checking to verification of practical systems is its high computational cost: the cardinality of a system's state space is typically exponential in the size of the input specification describing the system's behavior, a phenomenon commonly known as state space explosion. In addition, the state space is not necessarily finite, in particular for real-time systems, where continuous variables with time dimension are part of the specification. Therefore, to make the problem more tractable, advanced model checkers rely on symbolic techniques, where, instead of individual states, sets of states are considered during state space traversal; and abstraction, where only parts of the system that are relevant for the requirement are considered. As a result, the abstracted system is a simpler system whose behavior overapproximates that of the original system, therefore, if the abstract system is correct, so is the original one. However, as the abstracted system might admit false negatives, that is, spurious faulty behavior that is not present in the original system, the key challenge is finding the right abstraction granularity. This process can be automated using abstraction refinement techniques: in case of a false negative, the abstraction is refined in a way that excludes the discovered faulty behavior. Our goal is to prov [...]
doi:10.5281/zenodo.4759046 fatcat:3vrprqrhfjeknjjdn74uqoreo4